In this work, we give parallel transport frame of a curve and we introduce the relations between the frame and Frenet frame of the curve in 4-dimensional Euclidean space. The relation which is well known in Euclidean 3-space is generalized for the …rst time in 4-dimensional Euclidean space. Then we obtain the condition for spherical curves using the parallel transport frame of them. The conditi...

For P 2 Z[x], let kPk denote the Euclidean norm of the coe cient vector of P . For an algebraic number , with minimal polynomial A, de ne the Euclidean norm of by k k = kkAk ; where k is the smallest positive integer for which kA 2 Z[x]. De ne the minimal Euclidean norm of by k k min = min kPk : P 2Z[x]; P ( ) = 0; P 6 0 : Given an algebraic number , we show there exists a P 2 Z[x] with P ( ) =...

We provide a new event-triggered delay compensation approach for linear systems with arbitrarily long constant input delays. Our prediction map is expressible as solution of discrete time system. method ensures input-to-state stability. also an analog under measurement delays, where the continuous-discrete Significant novel features are our combined use matrices absolute values and based event ...

Abstract In this paper, I outline and defend the view that variations in compliance levels with one same norm represent different norms about following . support of claim, first argue classic game-theoretic accounts, which define as Nash equilibria noncooperative games, typically consider separate norms. After that, suggest a more fine-grained, distinction accounts for degrees show how to incor...

We present an efficient algorithm to compute the induced norms of finite-horizon Linear Time-Varying (LTV) systems. The formulation includes both L2 and terminal Euclidean norm penalties on outputs. Existing computational approaches include power iteration bisection a Riccati Differential Equation (RDE). has low computation time per but overall convergence can be slow. In contrast, RDE conditio...

We propose a new output event-triggered control design for linear discrete-time systems with constant arbitrarily long input delays, using delay compensating subpredictors. prove input-to-state stability of the closed loop system, framers and theory positive systems. A novel feature our approach is use matrices absolute values, instead Euclidean norms, in event triggers design. illustrate model...

This paper presents a new design for the event-triggered output feedback control of uncertain linear time-varying systems. Departing from traditional treatments time-invariant systems, it is shown that factoring fundamental solutions as products matrix differential equations, together with small-gain arguments and notions interval observers positive lead to class robust output-feedback controll...

In this article, we study necessary and sufficient conditions for contraction incremental stability of dynamical systems with respect to non-Euclidean norms. First, introduce weak pairings as a framework contractivity arbitrary norms, characterize their properties. We the sign max <tex-math...